Forward and inverse problems in towed cable hydrodynamics

Abstract

Abstract. This paper addresses the problem of reconstructing the velocities of the ocean currents impinging on a towed streamer cable during an offshore seismic survey. This study considers a two-dimensional model describing the motion of a flexible, inextensible cable in the presence of hydrodynamic drag forces in an incompressible fluid. In the first part the forward model is introduced and then solved to yield the cable's velocity, curvature and tension in the knowledge of the towing vessel motion and the hydrodynamic loads applied. In sequence, we formulate the inverse problem of inferring the ocean current velocities from discrete samples of the cable's shape and tension and show that this is rank deficient and ill-posed. In approaching the inverse problem a numerically stable algorithm is adopted based on generalized Tikhonov regularization, in the context of robust differentiation of discrete noisy signals. In order to demonstrate the practical performance of the scheme, some examples of ocean current reconstructions obtained using simulated noisy data are presented.

The vertical shape of a buoyant acoustic streamer between depth control units

“…The following conditions at the tail extend the two dimensional boundary conditions found in Polydorides et al (2008Polydorides et al ( , 2009). The tail buoy is assumed to provide T L ¼ 2000 N of drag when its speed through the water is α ¼ 2:5722 m/s (5 knots), leading to the following relation:…”

“…Choosing the following representative parameter values (these are the drag coefficients and diameter used to model a streamer in Polydorides et al, 2008) g ¼ À9:81 m s À 2 ; V ¼ 2:57 m s À 1 ;…”

Marine Electrical Sensing for Detecting Small Inhomogeneities

“…The location of the current source function and the coordinates of the electrodes that measure u depend on the position and shape of the cable at any given time. Assuming that the velocity of the towing vessel is kept almost constant in magnitude, the motion of the cable can be approximated by the linear hydrodynamic model [23] …”

“…Under conditions (6)- (13), the motion of the cable is uniquely determined to yield the coordinates of the applied currents and measured voltages, within the numerical error margin [23]. In addition to the electrical measurements, data acquisition also involves positioning measurements of the electrodes in short regular time intervals.…”

Ocean current prediction in towed cable hydrodynamics under dynamic steering

“…Evidently, the introduction of SE essentially transforms the inverse problem from quasi-linear and mildly ill-posed to nonlinear ill-posed, distorting at the same time the otherwise smooth curvature of the cable with severe consequences on the differentiability of the forward data. The variant problem formulation, which requires the recovery of the OCVP without any steering is linear and the forward variables (signals) are continuous in space, allowing the implementation of smooth inversion methods as this has been addressed in (12).…”